Kelley's formula as a basis for the assessment of reliable change

In the literature on the measurement of change, reliable change is usually determined by means of a confidence interval around an observed value of a statistic that estimates the true change. In recent literature on the efficacy of psychotherapies, attention has been particularly directed at the improvement of the estimation of the true change. Reliable Change Indices, incorporating the reliability-weighted measure of individual change, also known as Kelley's formula, have been proposed. According to current practice, these indices are defined as the ratio of such an estimator and an intuitively appealing criterion and then regarded as standard normally distributed statistics. However, because the authors fail to adopt an adequate standard error of the estimator, the statistical properties of their indices are unclear. In this article, it is shown that this can lead to paradoxical conclusions. The adjusted standard error is derived.